Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x+6y &= 9 \\ 5x-2y &= -6\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $-2y = -5x-6$ Divide both sides by $-2$ to isolate $y$ $y = {\dfrac{5}{2}x + 3}$ Substitute this expression for $y$ in the first equation. $-5x+6({\dfrac{5}{2}x + 3}) = 9$ $-5x + 15x + 18 = 9$ Simplify by combining terms, then solve for $x$ $10x + 18 = 9$ $10x = -9$ $x = -\dfrac{9}{10}$ Substitute $-\dfrac{9}{10}$ for $x$ back into the top equation. $-5( -\dfrac{9}{10})+6y = 9$ $\dfrac{9}{2}+6y = 9$ $6y = \dfrac{9}{2}$ $y = \dfrac{3}{4}$ The solution is $\enspace x = -\dfrac{9}{10}, \enspace y = \dfrac{3}{4}$.